(^24) A Textbook of Engineering Mechanics
- Use of Bow’s notations. All the forces in the space diagram are named by using the Bow’s
notations. It is a convenient method in which every force (or load) is named by two capital
letters, placed on its either side in the space diagram. - Construction of vector diagram (force diagram). It means the construction of a diagram
starting from a convenient point and then go on adding all the forces vectorially one by one
(keeping in veiw the directions of the forces) to some suitable scale.
Now the closing side of the polygon, taken in opposite order, will give the magnitude of the
resultant force (to the scale) and its direction.
Example 2.10. A particle is acted upon by three forces equal to 50 N, 100 N and 130 N,
along the three sides of an equilateral triangle, taken in order. Find graphically the magnitude and
direction of the resultant force.
Solution. The system of given forces is shown in Fig. 2.8 (a)
First of all, name the forces according to Bow’s notations as shown in Fig. 2.8 (a). The 50 N
force is named as AD, 100 N force as BD and 130 N force as CD.
Fig. 2.8.
Now draw the vector diagram for the given system of forces as shown in Fig. 2.8 (b) and as
discussed below :- Select some suitable point a and draw ab equal to 50 N to some suitable scale and parallel
to the 50 N force of the space diagram. - Through b, draw bc equal to 100 N to the scale and parallel to the 100 N force of the space
diagram. - Similarly through c, draw cd equal to 130 N to the scale and parallel to the 130 N force of
the space diagram. - Join ad, which gives the magnitude as well as direction of the resultant force.
- By measurement, we find the magnitude of the resultant force is equal to 70 N and acting
at an angle of 200° with ab. Ans.
Example 2.11 The following forces act at a point :
(i) 20 N inclined at 30° towards North of East.
(ii) 25 N towards North.
(iii) 30 N towards North West and
(iv) 35 N inclined at 40° towards South of West.
Find the magnitude and direction of the resultant froce.
*Solution. The system of given forces is shown in Fig. 2.9 (a).
- We have already solved this example analytically as example 2.7.